Prediction of ship maneuvering motion in regular wave with gray-box modelling

Objectives Aiming at the requirement of real-time and accurate prediction of ship maneuvering motion, the prediction of ship maneuvering motion in regular wave is investigated with gray-box modelling to improve the accuracy. Methods The equation of maneuvering motion is proposed to reveal the known movement mechanism. The hydrodynamic forces in calm water are approximated by taking the Taylor series expansion and the second-order steady wave drift forces are estimated with empirical formulas, then the mathematical model for predicting the ship maneuvering motion in regular wave is obtained. To promote the precision of the hydrodynamic expression, the Fourier transform method is adopted to separate the data of maneuvering and seakeeping motions, then the model for hydrodynamic correction and second-order steady wave drift forces which is developed based on the data of maneuvering motion and Deep Neural Network (DNN) is submitted into the mechanistic equation of maneuvering motion, ultimately, the gray-box modelling incorporating mechanism and data for predicting the ship maneuvering motion in regular wave is innovatively established. Results Taking the Office of Naval Research Tumblehome (ONRT) as an example, the maneuvering motion is predicted with the adoptions of mathematical model and gray-box model respectively. For all the simulated cases, the simulation of unit time step costs 2~3 millisecond averagely, the average error between the results of gray-box model and tests is 5.17%, the accuracy is promoted averagely 4.50% compared with the mathematical model. Conclusions The gray-box modelling can be recognized as an efficient method for predicting the ship maneuvering motion, which lay a foundation for the real-time prediction of maneuvering motion in real marine environment.